Splitting the center of a Sylow subgroup
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911414089678848 |
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| author | Glauberman, George Lynd, Justin |
| author_facet | Glauberman, George Lynd, Justin |
| contents | Suppose $p$ is a prime and $S$ is a Sylow $p$-subgroup of a finite group $G$. If $S$ is normal in $G$, then $Z(S)$ is the direct product of $S \cap Z(G)$ with $[Z(S), G]$. We prove an analogous result for all groups except in some cases where $p=2$ and $G$ is not solvable, where we have counterexamples. We also extend this result to fusion systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01197 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Splitting the center of a Sylow subgroup Glauberman, George Lynd, Justin Group Theory 20D20 Suppose $p$ is a prime and $S$ is a Sylow $p$-subgroup of a finite group $G$. If $S$ is normal in $G$, then $Z(S)$ is the direct product of $S \cap Z(G)$ with $[Z(S), G]$. We prove an analogous result for all groups except in some cases where $p=2$ and $G$ is not solvable, where we have counterexamples. We also extend this result to fusion systems. |
| title | Splitting the center of a Sylow subgroup |
| topic | Group Theory 20D20 |
| url | https://arxiv.org/abs/2602.01197 |